Quantum field theory

Physics, Second Cycle
1 year
Lecturer (contact person):
Hours per week – 1. semester:

Enrollment into the program.
Positive result from qoloqia (or written exam) is necessary to enter the oral exam.

Content (Syllabus outline)

Probelms with relativistic quantum mechanics and the need for quantum field theory, causality
Classical field theory, Noether theorem, conserved current and charge, tensor of energy and momentum
Canonical quantization of relativistic free scalar field, Kline Gordon equation, propagator; nonrelativistic example of one-dimensional harmonic chain (phonons); complex scalar field
Transformations of vector and spinor fields under Lorentz transformations (boosts, rotations and their combinations), generators
Free Dirac field: Dirac equation, clasical field and canonical quantization, operator of charge, momentum and angular momentum, spin, antiparticles, propagators, difference between Dirac and Majorana fermions
Free electromagnetic field, clasical gauge theory, (naive) quantization
Various field theoreis with interactions between scalars, spinors and vectors, gauge transformations and interaction in electrodynamics, perturbation theory, interaction picture, correlation functions, Wick's theorem, Feynman rules
Scattering and S-matrix and their relation to correlation functions (LSZ theorem), Feynman diagrams
Scattering at lowest order: examples for electrodynamics, scalar phi^4 theory and theory with interactions between scalars and fermions
Feynman path integral in scalar quantum field theory; application at zero temperature and at finite temperature; Matsubara frequencies, partition function for free bosons in both cases
Perturbative corrections at one-loop order for electrodynamics (electron and photon self-energy and vertex correction): dimensional regularization, Wick rotation, renormalization with the ordinary and counter term methods, field strength renormalization, renormalization of n-point correlation functions, observable consequences in QED: anomalous magnetic moment, running of coupling (e) with energy, Lamb shift, LSZ theorem in more detail
Renormalization group equations; running couplings
Kosterlitz-Thouless transition, example of two-dimensional XY model, vortices

  • M. Peskin, D. Schroeder: An introduction to quantum field theory, Addison-Wesley publishing company, New York, 1995
  • Claude Itzykson, Jean-Bernard Zuber: QuantumField Theory
    McGraw-Hill, New York, 1987

  • A. Altland, B. Simons, Condensed Matter Field Theory, Cambridge University Press , 2010

Objectives and competences


Student gets familiar with the properties of free quantum fields, their interactions and symetry properties.
Knowledge and understanding of basic principles of quantum field theory, quantisation approaches, principlesof gauge interactions .

Intended learning outcomes

Knowledge and understanding:

Knowledge of basic tyheoretical tools in elementary particle physics, with additional applications applications to condensed matter systems.
The achieved knowledge enables student to solve theoretical problems within field elementary particle theory and examples of filed-theory applications in condesed matter systems.
Critical evalvation of theoretical approaches within relativistic and quantum physics.
Transferable skills:
Ability to construct theoretical models and analyze physical problems in theoretical high energy physics. Ability for application of field theory for non-relativistic problems in other fields of physics.

Learning and teaching methods

Lectures, exercises, seminars, homework, consultations


2 midterm exams instead or final written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Sasa Prelovsek (ime v clankih)
(1) Approximate degeneracy of J = 1 spatial correlators in high temperature QCD
C. Rohrhofer, Y. Aoki, G. Cossu, H. Fukaya, L. Glozman, S. Hashimoto, C. Lang, S. Prelovsek Phys. Rev. D 96, 094501 (2017)
(2) Ds0∗ (2317) meson and DK Scattering from Lattice QCD D. Mohler, C.B. Lang, L. Leskovec, S. Prelovsek, R.M. Woloshyn Phys. Rev. Lett. 111 (2013) 222001
(3) Evidence for X(3872) from DD* scattering on the lattice S. Prelovsek , L. Leskovec
Phys. Rev. Lett. 111 (2013) 192001
(4) Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD
L. Leskovec, S. Prelovsek Phys.Rev. D85 (2012) 114507
(5) Coupled channel analysis of the rho meson decay in lattice QCD C.B. Lang, D. Mohler, S. Prelovsek, M. Vidmar Phys. Rev. D84 (2011) 054503